OSCILLATION is the process of moving back and forth of a body about a mean position. For example, Movement of the pendulum after a small deviation from its mean position (equilibrium position).Underdamped harmonic oscillations are those types of harmonic oscillations in which the amplitude of oscillation decreases with time because of the energy loss due to friction.Resonance:When an external vibrating system causes another system to oscillate with greater amplitude at a specific frequency, the phenomenon is called resonance, and that specific frequency is called resonant frequency. Resonance occurs when external system frequency and undamped NATURAL frequency both are equal.\(Frequency\;RATIO = \;\FRAC{{Frequency\;of\;external\;vibrating\;system}}{{Natural\;frequency\;of\;system}} = \;\frac{\omega }{{{\omega _n}}}\)\(Damping\;Ratio\;(\zeta) = \;\frac{{Damping\;coefficient}}{{Critical\;damping\;coefficient}} = \;\frac{C}{{{C_c}}}\)If damping ratio ζ < 1 system will be underdamped, ζ = 1 system will be critically damped, ζ > 1 system will be overdamped.